Mathematical models for the synthesis and optimization of spiral bevel gear tooth surfaces

The geometry of spiral bevel gears and to their rational design are studied. The nonconjugate tooth surfaces of spiral bevel gears are, in theory, replaced (or approximated) by conjugated tooth surfaces. These surfaces can be generated by two conical surfaces, and by a conical surface and a revolution. Although these conjugated tooth surfaces are simpler than the actual ones, the determination of their principal curvatures and directions is still a complicated problem. Therefore, a new approach, to the solution of these is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the generated gear surface are obtained. With the aid of these analytical tools, the Hertzian contact problem for conjugate tooth surfaces can be solved. These results are useful in determining compressive load capacity and surface fatigue life of spiral bevel gears. A general theory of kinematical errors exerted by manufacturing and assembly errors is developed. This theory is used to determine the analytical relationship between gear misalignments and kinematical errors. This is important to the study of noise and vibration in geared systems

Kinematic precision of gear trains

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory

Precision of spiral-bevel gears

The kinematic errors in spiral bevel gear trains caused by the generation of nonconjugate surfaces, by axial displacements of the gears during assembly, and by eccentricity of the assembled gears were determined. One mathematical model corresponds to the motion of the contact ellipse across the tooth surface, (geometry I) and the other along the tooth surface (geometry II). The following results were obtained: (1) kinematic errors induced by errors of manufacture may be minimized by applying special machine settings, the original error may be reduced by order of magnitude, the procedure is most effective for geometry 2 gears, (2) when trying to adjust the bearing contact pattern between the gear teeth for geometry 1 gears, it is more desirable to shim the gear axially; for geometry II gears, shim the pinion axially; (3) the kinematic accuracy of spiral bevel drives are most sensitive to eccentricities of the gear and less sensitive to eccentricities of the pinion. The precision of mounting accuracy and manufacture are most crucial for the gear, and less so for the pinion

Letter to the Editor of Journal of Otolaryngology regarding “Risk of diabetes in patients with sleep apnea: comparison of surgery versus CPAP in a long-term follow-up study”

Abstract Obstructive sleep apnea (OSA) is associated with multiple chronic comorbidities with treatments including continuous positive airway pressure (CPAP), upper airway surgery (UAS), and hypoglossal nerve stimulation (HNS). Given the complexity of the condition and multiple treatment options, there is an ongoing debate to determine the best management. O’Connor-Reina et al. recently published a paper titled “Risk of diabetes in patients with sleep apnea: comparison of surgery versus CPAP in a long-term follow-up study.” In their study, the authors stated that OSA patients who received surgery had a 50% less chance of developing diabetes compared to patients who only received CPAP treatment. However, we would like to point out some limitations that warrant attention and caution interpretation of the findings by physicians and patients

Extremity Findings of Methotrexate Embryopathy

© The Author(s) 2019. Background: Methotrexate (MTX) is widely used as an immunosuppressant, chemotherapeutic, and abortifacient agent. It is also a potent teratogen, and intentional or unintentional exposure during pregnancy is associated with heterogeneous birth anomalies. Methods: We retrospectively reviewed a cohort of patients who presented to our clinic with limb anomalies in the setting of MTX embryopathy. Results: In our case series, we describe 7 cases of patients who had limb anomalies with heterogeneous functionality, from severely debilitating to completely asymptomatic. Most of the upper extremity anomalies in our group were managed conservatively. Conclusions: Methotrexate embryopathy is a rare but clinically important entity with phenotypic and functional variability. This series underscores the need for proper counseling of patients and raises concern regarding using this medication for the purpose of abortion

Occult Scaphocephaly: A Forme Fruste Phenotype of Sagittal Craniosynostosis

INTRODUCTION: Latent cranial suture fusions may present with mild or absent phenotypic changes that make the clinical diagnosis challenging. Recent reports describe patients with sagittal synostosis and a normal cranial index (CI), a condition termed normocephalic sagittal craniosynostosis (NSC). The goal of this study is to evaluate the shape and intracranial volume (ICV) in a cohort of NSC patients using quantitative cranial shape analysis (CSA). METHODS: We identified 19 patients (7.5 ± 2.28 years) between 2011 and 2016, who presented to our hospital with NSC. Cranial index and CSA were measured from the computed tomography image. Cranial shape analysis calculates the distances between the patient\u27s cranial shape and its closest normal shape. Intracranial volume was measured and compared to an established age-matched normative database. RESULTS: Cranial index revealed 15 (78.9%) patients within the mesocephalic range and 4 patients (21.1%) in the brachycephalic range. Detailed CSA identified 15 (78.9%) patients with subtle phenotypic changes along the scaphocephalic spectrum (ie, subtle anterior and posterior elongation with inter-parietal narrowing) and 1 patient (5.3%) with isolated overdevelopment on the posterior part of the right parietal bone. Three patients (15.8%) had a CSA close to normal. Mean ICV was 1410.5 ± 192.77cc; most patients (78.9%) fell within ±2 standard deviations. CONCLUSION: Quantitative CSA revealed that most of the patients with NSC had cranial shape abnormalities, consistent with a forme fruste scaphocephaly that could not be otherwise recognized by clinical observation or CI. Given these findings, we propose the term occult scaphocephaly to describe this condition. The associated incidence of intracranial hypertension is unknown